Remove texture from object
Blender sometimes doesn't remove textures properly, and it requires several attempts to save and reload the blend file before they are removed permanently. To be sure that they are removed properly, do the following:

1) Go into the Properties editor > Textures context, highlight the texture you want to remove.



2) Click on the X button to the right of the field for the texture's datablock ID name: This will unlink it from the object it was assigned to, but it still remains in the blend file. To unlink the datablock from ALL objects in the file, hold down the Shift key while clicking on it. 



3) Check your object. If you still see the texture on it, select the object and go into edit mode. Now select one of the faces that the texture is on. 

4) Open the UV Map editor and check to see if the texture image is visible there. If it is, then go to the field in the menu header where the name of the texture's datablock ID is listed, and click on the X button to the right of it. When you do, your object should no longer be showing the texture:



5) In the Outliner window, change the display type in the header menu from All Scenes (or whatever you have it set to) to Orphaned Data



6) If there are any sub-menus listed for materials or images, open them and check to make sure that none of them have green checkmarks beside them. If they do, LMB click on the checkmark to remove it. 



7) Now save the file and reload it. Look in the Outliner again to see if all the orphaned data has been removed. If it hasn't, continue to save and reload the file until it's all gone. 

You should now have no problems with that texture. 

NOTE: Never delete materials that have textures assigned to them unless you have unlinked the textures first.